Waveform inversion
can be described as iteratively migrating waveform residuals into the medium, where the slowness
field is updated by the misfit migration image.
In fact, the first iteration of waveform inversion is equivalent to the
migration of seismic data.
Waveforms are rich in detailed information about the earth's velocity and density
distributions at intermediate and high wavenumbers
(Jannane et al., 1989), but also tend to make the misfit function highly non-linear.
Thus, the starting model should be somewhat close to the actual model
at the low and intermediate wavenumber levels (Sneider et al., 1989; Landa et al., 1989).
Compared
to migration, waveform tomography is not as robust, is computationally
much more expensive and requires an expert to get it to work.
Thus, future research should aim towards mitigating these problems and
attempt to make tomography as effective and as easy to use as migration.
The payoff will be more accurate estimates
of lithology than provided by either migration or AVO (Amplitude vs Offset) studies.